Sample QuestionsExponents Of Real Numbers questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $8^{x+1}=64$, what is the value of $3^{2 x+1}$ ?
Answer: D.
View full solution →$(256)^{0.16} \times(256)^{0.09}$
Answer: A.
View full solution →The value of $64^{-\frac{1}{3}}\Big(64^{\frac{1}{3}}-64^{\frac{2}{3}}\Big)$ is:
Answer: C.
View full solution →If $\frac{3^{5\text{x}}\times81^2\times6561}{3^{2\text{x}}}$ then $x =$
- A
$3$
- ✓
$-3$
- C
$\frac{1}{3}$
- D
$-\frac{1}{3}$
Answer: B.
View full solution →If $\sqrt{2^\text{n}}=1024,$ then $3^{2\Big(\frac{\text{n}}{4}-4\Big)}=$
Answer: B.
View full solution →Statement-1 (A): If $(16)^{2 x+3}=(64)^{x+3}$, then $4^{2 x-2}=256$.
Statement-2 (R): If $a \neq 0, \pm 1$, then $a^m=a^n \Rightarrow m=n$ and $\left(a^m\right)^n=a^{m n}$.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-3
- C
Statement-1 is True, Statement-2 is False
- D
Statement-1 is False, Statement-2 is True
Answer: A.
View full solution →Statement-1 $(A): \left\{\left(a^{-1}+b^{-1}\right)\left(a^{-1}-b^{-1}\right)\right\} \div\left\{\left(\frac{1}{a^{-1}}-\frac{1}{b^{-1}}\right)\left(\frac{1}{a^{-1}}+\frac{1}{b^{-1}}\right)\right\}=1$.
Statement-2 ( $R$ ): For any $a \neq 0, a^{-m}=\frac{1}{a^m}$ and $a^m=\frac{1}{a^{-m}}$.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-2
- C
Statement-1 is True, Statement-2 is False
- ✓
Statement-1 is False, Statement-2 is True
Answer: D.
View full solution →Statement-1 (A): $\sqrt{\frac{81}{64} \sqrt{\frac{81}{64} \sqrt{\frac{81}{64} \sqrt{\frac{81}{64}}}}} \cdots \cdot x=\frac{9}{8}$,
Statement-2 (R): For any positive real number $x: \sqrt{x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}}} \ldots x=x$.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1
- ✓
Statement-1 is True, Statement-2 is False
- D
Statement-1 is False, Statement-2 is True
Answer: C.
View full solution →Statement-1 (A): If m, n are positive integers, then for any positive real number a, $\{\sqrt[m]{\sqrt[n]{a}}\}^{m n}=a$
Statement-2 (R): If m, n, p are rational numbers and a is any positive real number, then $\left(\left(a^m\right)^n\right)^p=a^{m n p}$.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): $\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+}}}} \ldots \ldots \ldots \ldots \infty=3$.
Statement-2 (R): $\sqrt{x+\sqrt{x+\sqrt{x+}}} \ldots \ldots \ldots \ldots \infty=x, x>0$.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: C.
View full solution →The value of $(256)^{0.16} \times(256)^{0.09}$ is _______________ .
View full solution →$\sqrt[4]{(81)^{-2}}$ is equal $t$ _______________ .
View full solution →The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ is equal to _______________ .
View full solution →$\sqrt[4]{\sqrt[3]{2^2}}$ equals _______________ .
View full solution →If $6^{x-y}=36$ and $3^{x+y}=729$, then $x^2-y^2=$ _______________ .
View full solution →If $a=3$ and $b=-2$, find the values of:
$a+b^{a b}$
View full solution →If $a = 3$ and $b = -2,$ find the values of:
$\text{a}^\text{b}+\text{b}^\text{a}$
View full solution →Simplify the following:
$\left(2 x^{-2} y^3\right)^3$
View full solution →If $a = 3$ and $b = -2,$ find the values of:
$\text{a}^\text{a}+\text{b}^\text{b}$
View full solution →If $493992=a^4 b^2 c^3$, find the values of $a, b$ and $c$ are and are different positive primes.
View full solution →Simplify the following: $\frac{(4\times10^7)(6\times10^5)}{8\times10^4}$
View full solution →Solve the following equations: $3^{\text{x}-1}\times5^{2\text{y}-3}=225$
View full solution →If $\text{x}=2^{\frac{1}{3}}+2^{\frac{2}{3}},$ show that $\text{x}^3-6\text{x}=6$
View full solution →Show that:$\frac{1}{1+\text{x}^{\text{a}+\text{b}}}+\frac{1}{1+\text{x}^{\text{b}-\text{c}}}=1$
View full solution →Solve the following equations for $x:$
$2^{\text{x}+1}=4^{\text{x}-3}$
View full solution →Simplify: $\Big(\frac{\sqrt{2}}{5}\Big)^8\div\Big(\frac{\sqrt{2}}{5}\Big)^{13}$
View full solution →Prove that: $\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\frac{1}{\Big(\frac{256}{625}\Big)^\frac{1}{4}}+\Big(\frac{\sqrt{25}}{\sqrt[3]{64}}\Big)^0=\frac{61}{16}$
View full solution → Show that:$\Big(\frac{\text{a}^{\text{x}+1}}{\text{a}^{\text{y}+1}}\Big)^{\text{x}+\text{y}}\Big(\frac{\text{a}^{\text{y}+2}}{\text{a}^{\text{z}+2}}\Big)^{\text{y}+\text{z}}\Big(\frac{\text{a}^{\text{z}+3}}{\text{a}^{\text{x}+3}}\Big)^{\text{z}+\text{x}}=1$
View full solution →If $3^{4\text{x}}=(81)^{-1}$ and $10^{\frac{1}{\text{y}}}0.0001,$ find the value of $2^{-\text{x}+4\text{y}}.$
View full solution →Prove that: $\frac{2^\text{n}+2^{\text{n-1}}}{2^{\text{n}+1}-2^\text{n}}=\frac{3}{2}$
View full solution →Prove that: $\Big(\frac{1}{4}\Big)^{-2}-3\times8^{\frac{2}{3}}\times4^0+\Big(\frac{9}{16}\Big)^{-\frac{1}{2}}=\frac{16}{3}$
View full solution →Solve the following equations:
$8^{\text{x}+1}=16^{\text{y}+2}$ and $\Big(\frac{1}{2}\Big)^{3+\text{x}}=\Big(\frac{1}{4}\Big)^{3\text{y}}$
View full solution →For any positive real number $x$, find the value of $\Big(\frac{\text{x}^{\text{a}}}{\text{x}^{\text{b}}}\Big)^{\text{a}+\text{b}}\times\Big(\frac{\text{x}^{\text{b}}}{\text{x}^{\text{c}}}\Big)^{\text{b}+\text{c}}\times\Big(\frac{\text{x}^{\text{c}}}{\text{x}^{\text{a}}}\Big)^{\text{c}+\text{a}}$
View full solution →Simplify $\Big[\Big\{(625)^{\frac{1}{2}}\Big\}^{-\frac{1}{4}}\Big]^2$
View full solution →Simplify:$\sqrt[\text{lm}]{\frac{\text{x}^\text{l}}{\text{x}^\text{m}}}\times\sqrt[\text{mn}]{\frac{\text{x}^\text{m}}{\text{x}^\text{n}}}\times\sqrt[\text{nl}]{\frac{\text{x}^\text{n}}{\text{x}^\text{l}}}$
View full solution →